The RZF combiner reduces to the ZF combiner as \(\lambda \rightarrow 0\) .
The inverse of the gram-matrix of the channel estimates exists with probability one when \( N \ge M_t^k \)  and \({\hat{\mathbf {H}}^{k}_t}\)  has full column rank.We note that the condition \( N \ge M_t^k \)  is not hard to satisfy in IRSA.
For example, with \(L = 2,3,4\) , each RE will be occupied by \(6,9,12\)  users on an average, respectively, if the average repetition factor is \(\bar{d} = 3 \) .
Thus any \(N\)  greater than, say, 16 would be sufficient to decode the users in most REs.
Hence, we can compute the combining matrix as
\({\mathbf {A}_t^k} = {\hat{\mathbf {H}}^{k}_t} ({\hat{\mathbf {H}}^{kH}_t} {\hat{\mathbf {H}}^{k}_t})^{-1}.\) 
Using the above, it is easy to show that the SINR expression simplifies as [1]}
\(\rho _{tm}^k = \dfrac{P g_{tm} }{ ( N_0 + \sum \nolimits _{i \in \mathcal {S}_k} P g_{ti} \delta _{ti}^{k} ) [ ({\hat{\mathbf {H}}^{kH}_t} {\hat{\mathbf {H}}^{k}_t})^{-1} ]_{mm} }. \) 
